To solve this problem, we need to calculate the total surface area of the 3D structure shown, where each small cube has a volume of $1 \, \text{cm}^3$. Since the volume of a cube is given by $\text{side}^3 = 1 \, \text{cm}^3$, the side length of each cube is $1 \, \text{cm}$.

Step 1: Count the number of visible cubes

The structure consists of $3 \times 3 \times 3 = 27$ cubes originally. However, there is an inner hollow part (a cube of $2 \times 2 \times 2 = 8$ cubes removed). Therefore, the total number of cubes in the structure is $27 - 8 = 19$.

Step 2: Determine the total surface area

Each cube has 6 faces, and since the cubes share faces, we need to account for only the visible faces. By examining the diagram, we count how many faces of the cubes are exposed to the outside.

• Top face: There are 9 cubes on the top, but the center cube is missing. So 8 cubes contribute 1 face each.
• Bottom face: Similarly, the bottom face has 8 exposed cubes.
• Front face: There are 5 exposed cubes in the front.
• Back face: The back also has 5 exposed cubes.
• Left side: 5 cubes are visible on the left side.
• Right side: The right side has 5 cubes visible.

Step 3: Calculate the total number of exposed faces

Adding up the number of exposed cubes on each face:

• Top: 8 cubes
• Bottom: 8 cubes
• Front: 5 cubes
• Back: 5 cubes
• Left: 5 cubes
• Right: 5 cubes

Thus, the total number of exposed faces is $8 + 8 + 5 + 5 + 5 + 5 = 36$.

Step 4: Multiply by the area of one face

Each face of a cube has an area of $1 \, \text{cm}^2$. Therefore, the total surface area is: $\text{Total surface area} = 36 \times 1 \, \text{cm}^2 = 36 \, \text{cm}^2.$

The closest answer available in the multiple-choice options is none of the given answers, as 36 cm² is not listed.

Do you want more details on any step? Here are five related questions:

1. How do you calculate the volume of a cube?
2. What is the formula for surface area of a cube?
3. How can you determine the surface area of a composite solid?
4. What happens to the surface area if we remove inner cubes from a structure?
5. How is the surface area affected by the number of exposed faces?

Tip: When solving surface area problems, always consider which faces are exposed, especially in hollow or composite structures.